Why mysql uses index with cardinality=1?

I created table categories:

 CREATE TABLE `categories` (
  `id` int NOT NULL AUTO_INCREMENT,
  `name` varchar(255) NOT NULL,
  `type` int unsigned NOT NULL,
  PRIMARY KEY (`id`),
  KEY `type` (`type`)
) ENGINE=InnoDB AUTO_INCREMENT=1100001 DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_0900_ai_ci

Then I filled table with random data:

<?php

$pdo = new PDO('mysql:host=localhost;dbname=test_perf', 'login', 'password');

$pdo->beginTransaction();
for ($i = 0; $i < 1000000; $i++) {
    $pdo->exec("INSERT INTO categories (name, type) VALUES ('" . uniqid() . "', 1)");
}
$pdo->commit();

Statistics for table indexes:

mysql> SHOW INDEXES FROM categories;
+------------+------------+----------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+---------------+---------+------------+
| Table      | Non_unique | Key_name | Seq_in_index | Column_name | Collation | Cardinality | Sub_part | Packed | Null | Index_type | Comment | Index_comment | Visible | Expression |
+------------+------------+----------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+---------------+---------+------------+
| categories |          0 | PRIMARY  |            1 | id          | A         |     1097250 |     NULL |   NULL |      | BTREE      |         |               | YES     | NULL       |
| categories |          1 | type     |            1 | type        | A         |           1 |     NULL |   NULL |      | BTREE      |         |               | YES     | NULL       |
+------------+------------+----------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+---------------+---------+------------+
2 rows in set (0,01 sec)

It`s right, index type has only one value (1).

Then I try select by type with ignore index(type):

mysql> select MAX(name) FROM categories ignore index(type) WHERE type=1;
+---------------+
| MAX(name)     |
+---------------+
| 6769b0dfec5e7 |
+---------------+
1 row in set (0,23 sec)

mysql> explain select MAX(name) FROM categories ignore index(type) WHERE type=1;
+----+-------------+------------+------------+------+---------------+------+---------+------+---------+----------+-------------+
| id | select_type | table      | partitions | type | possible_keys | key  | key_len | ref  | rows    | filtered | Extra       |
+----+-------------+------------+------------+------+---------------+------+---------+------+---------+----------+-------------+
|  1 | SIMPLE      | categories | NULL       | ALL  | NULL          | NULL | NULL    | NULL | 1097250 |   100.00 | Using where |
+----+-------------+------------+------------+------+---------------+------+---------+------+---------+----------+-------------+
1 row in set, 1 warning (0,00 sec)

And without it:

mysql> select MAX(name) FROM categories WHERE type=1;
+---------------+
| MAX(name)     |
+---------------+
| 6769b0dfec5e7 |
+---------------+
1 row in set (0,80 sec)

mysql> explain select MAX(name) FROM categories WHERE type=1;
+----+-------------+------------+------------+------+---------------+------+---------+-------+--------+----------+-------+
| id | select_type | table      | partitions | type | possible_keys | key  | key_len | ref   | rows   | filtered | Extra |
+----+-------------+------------+------------+------+---------------+------+---------+-------+--------+----------+-------+
|  1 | SIMPLE      | categories | NULL       | ref  | type          | type | 4       | const | 548625 |   100.00 | NULL  |
+----+-------------+------------+------------+------+---------------+------+---------+-------+--------+----------+-------+
1 row in set, 1 warning (0,00 sec)

As you can see, mysql uses index type, but it only degrades performance. At the same time, the statistics are correct.

Why mysql uses index type?
Mysql version: 8.0.35-0ubuntu0.22.04.1.

I expecting mysql should not use this index.